A novel multistable chaotic system with 2m-scroll attractor and its application

Recently, the construction of interesting chaotic systems has become an important and meaningful task. In this paper, based on the classical Jerk system, an improved Jerk chaotic system with extreme multistability is proposed by introducing the tangent function. The system can produce an infinite number of coexisting attractors. Additionally, the system exhibits intricate bifurcation behavior in the space of two parameters. Secondly, a chaotic system with a controllable amount of attractor scroll is initially designed based on a modified Jerk chaotic system by introducing fractal transformation. An unlimited number of coexisting four-scroll attractor, six-scroll attractor, eight-scroll attractor, and other unusual coexistence dynamics are discovered, which is interesting. Finally, a simple image encryption technique based on the scrambling–diffusion framework is designed using the proposed system. The experimental results demonstrate the effectiveness of the encryption scheme.